Browse · MATH Print → jmc number theory senior Problem Given that 8−1≡85(mod97), find 64−1(mod97), as a residue modulo 97. (Give an answer between 0 and 96, inclusive.) Solution — click to reveal Since 8−1≡85(mod97), 64−1≡(82)−1≡(8−1)2≡852≡47(mod97). Final answer 47 ← Previous problem Next problem →